1. Field
Embodiments described herein generally relate to fracture mechanics. More particularly, embodiments described herein relate to performing crack analyses using stress intensity factor calculations from non-singular finite elements.
2. Description of the Related Art
Fracture mechanics is an immensely powerful tool that allows rational predictions to be made with regard to the ultimate strength and residual fatigue life of cracked structures. Finite element techniques exist that are appropriate for the analysis of cracks, but they generally rely on the use of specialized crack tip elements. There is a fundamental problem though when it comes to modeling cracks, because the gradient of the stress/stain field is large and approaches infinity at the crack tip. To reproduce this behavior precisely with standard finite elements, an infinitesimally fine mesh would be required. The problem can be overcome with the use of singular, or quarter point, crack tip elements known in the art. These are formulated so that they contain a singularity similar to that found at the crack tip. Many standard finite element programs do not possess these elements, however. Moreover, the parameters needed for fracture mechanics calculations such as the stress intensity factor or the J integral can only be extracted from finite element results with specialized post processing algorithms. Such analyses remain the province of the specialist, therefore, restricting the application of fracture mechanics by the wider engineering community.
There is a need, therefore, for systems and methods that enable the determination of crack tip stress intensity factors for an arbitrarily shaped crack in an arbitrarily shaped solid without requiring the use of an extremely fine crack tip mesh, without the use of specialized crack tip elements, or without complex post processing, and which can be performed using standard finite element software packages known in the art.